Feature engineering for electricity load forecasting

The purpose of this notebook is to demonstrate how to use skrub and polars to perform feature engineering for electricity load forecasting.

We will build a set of features from different sources:

• Historical weather data for 10 medium to large urban areas in France;

• Holidays and calendar features for France;

• Historical electricity load data for the whole of France.

All these data sources cover a time range from March 23, 2021 to May 31, 2025.

Since our maximum forecasting horizon is 24 hours, we consider that the future weather data is known at a chosen prediction time. Similarly, the holidays and calendar features are known at prediction time for any point in the future.

Therefore, features derived from the weather and calendar data can be used to engineer “future covariates”. Since the load data is our prediction target, we will can also use it to engineer “past covariates” such as lagged features and rolling aggregations.

Environment setup

We need to install some extra dependencies for this notebook if needed (when running jupyterlite). We need the development version of skrub to be able to use the skrub expressions.

%pip install -q https://pypi.anaconda.org/ogrisel/simple/polars/1.24.0/polars-1.24.0-cp39-abi3-emscripten_3_1_58_wasm32.whl
%pip install -q altair holidays https://pypi.anaconda.org/ogrisel/simple/skrub/0.6.dev0/skrub-0.6.dev0-py3-none-any.whl

ERROR: polars-1.24.0-cp39-abi3-emscripten_3_1_58_wasm32.whl is not a supported wheel on this platform.

Note: you may need to restart the kernel to use updated packages.

Note: you may need to restart the kernel to use updated packages.

# The following 3 imports are only needed to workaround some limitations
# when using polars in a pyodide/jupyterlite notebook.
import tzdata  # noqa: F401
import pandas as pd
from pyarrow.parquet import read_table

import polars as pl
import skrub
from pathlib import Path
import holidays

Time range

Let’s define a hourly time range from March 23, 2021 to May 31, 2025 that will be used to join the electricity load data and the weather data. The time range is in UTC timezone to avoid any ambiguity when joining with the weather data that is also in UTC.

We wrap the polars dataframe in a skrub variable to benefit from the built-in TableReport display in the notebook. Using the skrub expression system will also be useful later.

time_range_start = pl.datetime(2021, 3, 23, hour=0, time_zone="UTC")
time_range_end = pl.datetime(2025, 5, 31, hour=23, time_zone="UTC")
time = skrub.var(
    "time",
    pl.DataFrame().with_columns(
        pl.datetime_range(
            start=time_range_start,
            end=time_range_end,
            time_zone="UTC",
            interval="1h",
        ).alias("time"),
    ),
)
time

<Var 'time'>

Show graph

Result:

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To avoid network issues when running this notebook, the necessary data files have already been downloaded and saved in the datasets folder. See the README.md file for instructions to download the data manually if you want to re-run this notebook with more recent data.

data_source_folder = Path("../datasets")
for data_file in sorted(data_source_folder.iterdir()):
    print(data_file)

../datasets/README.md
../datasets/Total Load - Day Ahead _ Actual_202101010000-202201010000.csv
../datasets/Total Load - Day Ahead _ Actual_202201010000-202301010000.csv
../datasets/Total Load - Day Ahead _ Actual_202301010000-202401010000.csv
../datasets/Total Load - Day Ahead _ Actual_202401010000-202501010000.csv
../datasets/Total Load - Day Ahead _ Actual_202501010000-202601010000.csv
../datasets/weather_bayonne.parquet
../datasets/weather_brest.parquet
../datasets/weather_lille.parquet
../datasets/weather_limoges.parquet
../datasets/weather_lyon.parquet
../datasets/weather_marseille.parquet
../datasets/weather_nantes.parquet
../datasets/weather_paris.parquet
../datasets/weather_strasbourg.parquet
../datasets/weather_toulouse.parquet

List of 10 medium to large urban areas to approximately cover most regions in France with a slight focus on most populated regions that are likely to drive electricity demand.

city_names = [
    "paris",
    "lyon",
    "marseille",
    "toulouse",
    "lille",
    "limoges",
    "nantes",
    "strasbourg",
    "brest",
    "bayonne",
]

all_city_weather_raw = {}
for city_name in city_names:
    # all_city_weather_raw[city_name] = skrub.var(
        # f"{city_name}_weather_raw",
    all_city_weather_raw[city_name] = (
        pl.from_arrow(read_table(f"../datasets/weather_{city_name}.parquet"))
    ).with_columns(
        [
            pl.col("time").dt.cast_time_unit(
                "us"
            ),  # Ensure time column has the same type
        ]
    )

all_city_weather_raw["brest"]

shape: (38_688, 7)

time	temperature_2m	precipitation	wind_speed_10m	cloud_cover	soil_moisture_1_to_3cm	relative_humidity_2m
datetime[μs, UTC]	f32	f32	f32	f32	f32	f32
2021-01-01 00:00:00 UTC	null	null	null	null	null	null
2021-01-01 01:00:00 UTC	null	null	null	null	null	null
2021-01-01 02:00:00 UTC	null	null	null	null	null	null
2021-01-01 03:00:00 UTC	null	null	null	null	null	null
2021-01-01 04:00:00 UTC	null	null	null	null	null	null
…	…	…	…	…	…	…
2025-05-31 19:00:00 UTC	17.5175	0.0	12.0694	5.0	0.168	73.0
2025-05-31 20:00:00 UTC	16.2675	0.0	9.114471	99.0	0.168	77.0
2025-05-31 21:00:00 UTC	15.5175	0.0	7.559999	93.0	0.169	84.0
2025-05-31 22:00:00 UTC	15.5675	0.0	9.0	100.0	0.17	82.0
2025-05-31 23:00:00 UTC	15.5675	0.0	5.506941	100.0	0.171	81.0

all_city_weather_raw["brest"].drop_nulls(subset=["temperature_2m"])

shape: (36_744, 7)

time	temperature_2m	precipitation	wind_speed_10m	cloud_cover	soil_moisture_1_to_3cm	relative_humidity_2m
datetime[μs, UTC]	f32	f32	f32	f32	f32	f32
2021-03-23 00:00:00 UTC	4.628	null	10.086427	null	null	94.0
2021-03-23 01:00:00 UTC	5.028	0.0	11.183201	6.0	null	95.0
2021-03-23 02:00:00 UTC	5.078	0.0	10.966713	6.0	null	94.0
2021-03-23 03:00:00 UTC	4.628	0.0	10.464797	5.0	null	93.0
2021-03-23 04:00:00 UTC	4.428	0.0	10.464797	5.0	null	92.0
…	…	…	…	…	…	…
2025-05-31 19:00:00 UTC	17.5175	0.0	12.0694	5.0	0.168	73.0
2025-05-31 20:00:00 UTC	16.2675	0.0	9.114471	99.0	0.168	77.0
2025-05-31 21:00:00 UTC	15.5175	0.0	7.559999	93.0	0.169	84.0
2025-05-31 22:00:00 UTC	15.5675	0.0	9.0	100.0	0.17	82.0
2025-05-31 23:00:00 UTC	15.5675	0.0	5.506941	100.0	0.171	81.0

all_city_weather = time.skb.eval()
for city_name, city_weather_raw in all_city_weather_raw.items():
    all_city_weather = all_city_weather.join(
        city_weather_raw.rename(lambda x: x if x == "time" else x + "_" + city_name),
        on="time",
        how="inner",
    )

all_city_weather = skrub.var(
    "all_city_weather",
    all_city_weather,
)
all_city_weather

<Var 'all_city_weather'>

Show graph

Result:

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Calendar and holidays features

We leverage the holidays package to enrich the time range with some calendar features such as public holidays in France. We also add some features that are useful for time series forecasting such as the day of the week, the day of the year, and the hour of the day.

Note that the holidays package requires us to extract the date for the French timezone.

Similarly for the calendar features: all the time features are extracted from the time in the French timezone.

holidays_fr = holidays.country_holidays("FR", years=range(2019, 2026))

fr_time = pl.col("time").dt.convert_time_zone("Europe/Paris")
calendar = time.with_columns(
    [
        fr_time.dt.date().is_in(holidays_fr.keys()).alias("is_holiday_fr"),
        fr_time.dt.weekday().alias("day_of_week_fr"),
        fr_time.dt.ordinal_day().alias("day_of_year_fr"),
        fr_time.dt.hour().alias("hour_of_day_fr"),
    ],
)
calendar

<CallMethod 'with_columns'>

Show graph

Result:

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Electricity load data

Finally we load the electricity load data. This data will both be used as a target variable but also to craft some lagged and window-aggregated features.

load_data_files = [
    data_file
    for data_file in sorted(data_source_folder.iterdir())
    if data_file.name.startswith("Total Load - Day Ahead")
    and data_file.name.endswith(".csv")
]

electricity_raw = skrub.var(
    "electricity_raw",
    pl.concat(
        [
            pl.from_pandas(pd.read_csv(data_file, na_values=["N/A", "-"])).drop(
                ["Day-ahead Total Load Forecast [MW] - BZN|FR"]
            )
            for data_file in load_data_files
        ],
        how="vertical",
    ),
)
electricity_raw

<Var 'electricity_raw'>

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Result:

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electricity = (
    electricity_raw.with_columns(
        [
            pl.col("Time (UTC)")
            .str.split(by=" - ")
            .list.first()
            .str.to_datetime("%d.%m.%Y %H:%M", time_zone="UTC")
            .alias("time"),
        ]
    )
    .drop(["Time (UTC)"])
    .rename({"Actual Total Load [MW] - BZN|FR": "load_mw"})
    .filter(pl.col("time").dt.minute().eq(0))
    .filter(pl.col("time") >= time_range_start)
    .filter(pl.col("time") <= time_range_end)
    .select(["time", "load_mw"])
)
electricity

<CallMethod 'select'>

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Result:

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electricity.filter(pl.col("load_mw").is_null())

<CallMethod 'filter'>

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Result:

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electricity.filter(
    (pl.col("time") > pl.datetime(2021, 10, 30, hour=10, time_zone="UTC"))
    & (pl.col("time") < pl.datetime(2021, 10, 31, hour=10, time_zone="UTC"))
).skb.eval().plot.line(x="time:T", y="load_mw:Q")

electricity = electricity.with_columns([pl.col("load_mw").interpolate()])
electricity.filter(
    (pl.col("time") > pl.datetime(2021, 10, 30, hour=10, time_zone="UTC"))
    & (pl.col("time") < pl.datetime(2021, 10, 31, hour=10, time_zone="UTC"))
).skb.eval().plot.line(x="time:T", y="load_mw:Q")

Check that the number of rows matches our expectations based on the number of hours that separate the first and the last dates. We can do that by joining with the time range dataframe and checking that the number of rows stays the same.

assert (
    time.join(electricity, on="time", how="inner").shape[0] == time.shape[0]
).skb.eval()

Lagged features

We can now create some lagged features from the electricity load data.

We will create 3 hourly lagged features, 1 daily lagged feature, and 1 weekly lagged feature. We will also create a rolling median and inter-quartile feature over the last 24 hours and over the last 7 days.

def iqr(col, *, window_size: int):
    """Inter-quartile range (IQR) of a column."""
    return col.rolling_quantile(0.75, window_size=window_size) - col.rolling_quantile(
        0.25, window_size=window_size
    )


electricity_lagged = electricity.with_columns(
    [pl.col("load_mw").shift(i).alias(f"load_mw_lag_{i}h") for i in range(1, 4)]
    + [
        pl.col("load_mw").shift(24).alias("load_mw_lag_1d"),
        pl.col("load_mw").shift(24 * 7).alias("load_mw_lag_1w"),
        pl.col("load_mw")
        .rolling_median(window_size=24)
        .alias("load_mw_rolling_median_24h"),
        pl.col("load_mw")
        .rolling_median(window_size=24 * 7)
        .alias("load_mw_rolling_median_7d"),
        iqr(pl.col("load_mw"), window_size=24).alias("load_mw_iqr_24h"),
        iqr(pl.col("load_mw"), window_size=24 * 7).alias("load_mw_iqr_7d"),
    ],
)
electricity_lagged

<CallMethod 'with_columns'>

Show graph

Result:

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import altair


altair.Chart(electricity_lagged.tail(100).skb.eval()).transform_fold(
    [
        "load_mw",
        "load_mw_lag_1h",
        "load_mw_lag_2h",
        "load_mw_lag_3h",
        "load_mw_lag_1d",
        "load_mw_lag_1w",
        "load_mw_rolling_median_24h",
        "load_mw_rolling_median_7d",
        "load_mw_iqr_24h",
        "load_mw_iqr_7d",
    ],
    as_=["key", "load_mw"],
).mark_line(tooltip=True).encode(x="time:T", y="load_mw:Q", color="key:N").interactive()

Investigating outliers in the lagged features

Let’s use the skrub.TableReport tool to look at the plots of the marginal distribution of the lagged features.

from skrub import TableReport

TableReport(electricity_lagged.skb.eval())

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Let’s extract the dates where the inter-quartile range of the load is greater than 15,000 MW.

electricity_lagged.filter(pl.col("load_mw_iqr_7d") > 15_000)[
    "time"
].dt.date().unique().sort().to_list().skb.eval()

[datetime.date(2021, 12, 26),
 datetime.date(2021, 12, 27),
 datetime.date(2021, 12, 28),
 datetime.date(2022, 1, 7),
 datetime.date(2022, 1, 8),
 datetime.date(2023, 1, 19),
 datetime.date(2023, 1, 20),
 datetime.date(2023, 1, 21),
 datetime.date(2024, 1, 10),
 datetime.date(2024, 1, 11),
 datetime.date(2024, 1, 12),
 datetime.date(2024, 1, 13)]

We observe 3 date ranges with high inter-quartile range. Let’s plot the electricity load and the lagged features for the first data range along with the weather data for Paris.

altair.Chart(
    electricity_lagged.filter(
        (pl.col("time") > pl.datetime(2021, 12, 1, time_zone="UTC"))
        & (pl.col("time") < pl.datetime(2021, 12, 31, time_zone="UTC"))
    ).skb.eval()
).transform_fold(
    [
        "load_mw",
        "load_mw_iqr_7d",
    ],
).mark_line(
    tooltip=True
).encode(
    x="time:T", y="value:Q", color="key:N"
).interactive()

altair.Chart(
    all_city_weather.filter(
        (pl.col("time") > pl.datetime(2021, 12, 1, time_zone="UTC"))
        & (pl.col("time") < pl.datetime(2021, 12, 31, time_zone="UTC"))
    ).skb.eval()
).transform_fold(
    [f"temperature_2m_{city_name}" for city_name in city_names],
).mark_line(
    tooltip=True
).encode(
    x="time:T", y="value:Q", color="key:N"
).interactive()

Based on the plots above, we can see that the electricity load was high just before the Christmas holidays due to low temperatures. Then the load suddenly dropped because temperatures went higher right at the start of the end-of-year holidays.

So those outliers do not seem to be caused to a data quality issue but rather due to a real change in the electricity load demand. We could conduct similar analysis for the other date ranges with high inter-quartile range but we will skip that for now.

If we had observed significant data quality issues over extended periods of time could have been addressed by removing the corresponding rows from the dataset. However, this would make the lagged and windowing feature engineering challenging to reimplement correctly. A better approach would be to keep a contiguous dataset assign 0 weights to the affected rows when fitting or evaluating the trained models via the use of the sample_weight parameter.

Final dataset

We now assemble the dataset that will be used to train and evaluate the forecasting models via backtesting.

prediction_time = time = skrub.var(
    "prediction_time",
    pl.DataFrame().with_columns(
        pl.datetime_range(
            start=time_range_start + pl.duration(days=7),
            end=time_range_end - pl.duration(hours=24),
            time_zone="UTC",
            interval="1h",
        ).alias("prediction_time"),
    ),
)
prediction_time

features = (
    (
        prediction_time.join(
            electricity_lagged, left_on="prediction_time", right_on="time"
        )
        .join(all_city_weather, left_on="prediction_time", right_on="time")
        .join(calendar, left_on="prediction_time", right_on="time")
    )
    .drop("prediction_time")
    .skb.mark_as_X()
)
features

<CallMethod 'drop'>

Show graph

Result:

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horizon = 1
target_column_name = f"load_mw_horizon_{horizon}h"
target_df = prediction_time.join(
    electricity.with_columns(
        [pl.col("load_mw").shift(-horizon).alias(target_column_name)]
    ),
    left_on="prediction_time",
    right_on="time",
)
target = target_df[target_column_name].skb.mark_as_y()

from sklearn.ensemble import HistGradientBoostingRegressor
import threadpoolctl


with threadpoolctl.threadpool_limits(limits=1):
    predictions = features.skb.apply(
        HistGradientBoostingRegressor(
            random_state=0,
            learning_rate=skrub.choose_float(
                0.01, 0.9, default=0.1, log=True, name="learning_rate"
            ),
        ),
        y=target,
    )
predictions

<Apply HistGradientBoostingRegressor>

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Result:

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altair.Chart(
    pl.concat(
        [
            target_df.skb.eval(),
            predictions.rename({"load_mw_horizon_1h": "predicted_load_mw_horizon_1h"}).skb.eval(),
        ],
        how="horizontal",
    ).tail(1000)
).transform_fold(
    [target_column_name, "predicted_load_mw_horizon_1h"],
).mark_line(
    tooltip=True
).encode(
    x="prediction_time:T", y="value:Q", color="key:N"
).interactive()

from sklearn.model_selection import TimeSeriesSplit

ts_cv = TimeSeriesSplit(n_splits=5, max_train_size=None, gap=0)
predictions.skb.cross_validate(
    cv=ts_cv,
    scoring=[
        "neg_mean_absolute_error",
        "neg_mean_squared_error",
        "r2",
        "neg_mean_absolute_percentage_error",
    ],
    verbose=1,
    n_jobs=-1,
)

[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.

[Parallel(n_jobs=-1)]: Done   5 out of   5 | elapsed:    6.1s finished

	fit_time	score_time	test_neg_mean_absolute_error	test_neg_mean_squared_error	test_r2	test_neg_mean_absolute_percentage_error
0	1.083030	0.062902	-705.158615	-1.379352e+06	0.990154	-0.012300
1	1.454367	0.060979	-643.255148	-7.297992e+05	0.993331	-0.012359
2	1.792142	0.057958	-701.813963	-9.736808e+05	0.987212	-0.016302
3	2.039425	0.035568	-673.123493	-9.567402e+05	0.989488	-0.014070
4	1.991959	0.034253	-607.788750	-6.380088e+05	0.994321	-0.011670